Question

What set describes the zeroes of the function f(x )= 6πsin(4x) shown in the graph?

Answer 1

"
`[x|x=(k)/(4)\pi]` for every integer
`k`"

Explanation:

The function has zeroes at the x-intercepts in the graph.

If you look at the graph from 0 to
`\pi`, you will see that the graph cuts the x-axis at 4 points.

They are at half of
`(\pi)/(2)`, which is
`(\pi)/(4)`, at
`(\pi)/(2)`, at half point between
`(\pi)/(2)` and
`\pi`, which is at
`(3\pi)/(4)`, and at
`\pi`.

They are basically all multiples of
`(\pi)/(4)`.

Looking at the answer choices, the third choice is correct.

Plugging in k=1, k=2, k=3, and k=4 into the equation, we see that the zeroes are exactly what we saw. Also, the negative side of the function holds true as well.

Third answer choice is right.